A Bessel collocation method for solving fractional optimal control problems

In the present paper, we apply the truncated Bessel series approximation by using collocation scheme, for solving linear and nonlinear fractional optimal control problems (OCPs) indirectly. Therefore, the necessary (and also sufficient in most cases) optimality conditions are stated in a form of nonlinear (or linear) fractional two-point boundary value problem (TPBVP). For solving this mentioned TPBVP, we generalize a new numerical method (which is called the Bessel collocation method). One of the best advantages of this generalization is that, there is no need to use operational matrices of differentiation and also the new generalized idea can be implemented in any mathematical software. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.